#### MiningMath

Get the NPV upper bound better than the Best Case scenario!

Mima 249 views

The concept of cut-off grade has been conceived to delineate what is ore and waste, considering the life of mine. Usually, manual assumptions are made to pre-define what must be considered ore or not, while using the LG or Pseudoflow methodologies. These approaches do not consider the value of the money through time in the decision-making process, which could generate a whole different mining sequence due to the choices of what and when it should be mined. Another challenge, that is faced when planning projects which involve multiple destinations, blending constraints, restrict mining areas, and all the complexities present in a real global optimization. MiningMath allows for such Global Optimization and you can still combine it with your current strategies!

MiningMath has no pre-defined assumptions in order to identify the cut-off limit, which is based on a math optimization considering a discounted cash flow while respecting production capacity, blending constraints, vertical advances, widths, and any other assumption. Another key aspect in this regard is that MiningMath is not constrained by fixed pits, pushbacks, or phases. Instead, the mining sequence is an optimized output, which is a consequence of each set of parameters used, allowing more flexibility to find completely new solutions. The advantages of these differences are even more evident for more complex cases with multiple destinations, or complex constraints that could be neglected, hiding opportunities.

As the algorithm here has no manual destinations appointments, it always sends the less valuable blocks to the dump, considering the set of constraints imposed, what means that MiningMath tries to comply with all the constraints inserted, by respecting this priority orderto define an optimized cut-off that can meet all of the requirements and increase the NPV as a consequence of a global optimization. Meanwhile, blocks that have positive values when processed can also be discarded to increase NPV based on the minimum economic value (economic value cut-off) going to the plant at that a specific period. Scenarios without stockpiling policy could have even higher positive values going to the waste since they do not have any other destination. Considering these examples, MiningMath can deliver quite different results from what you were expecting from your previous assumptions. However, you can also get closer, as much as you wish, to any solution by using the approaches suggested below.

Forcing a cut-off grade on MiningMath will likely make you lose part of the advantages it can offer. However, for many reasons, mining professionals might still be willing to use either to compare different approaches, to understand the practical effects of using it, or not, etc. The approaches mentioned could also be used to forbid any material type on the plant, and the use of the item 2.1. could even reduce the complexity of the algorithm, since it could use fewer constraints to deal with it.

## Using Economic Values

You can create multiple columns of economic values, each one for a cut-off you want to test. Then, force MiningMath to use this limit by defining very negative values for the destination you want to avoid, as it is shown in Figure 1, for a cut-off of 0.5. The math is:

Economic Value Process = If [Ore_Grade] > [0.5], then [f(Economic Value)], else [-999,999,999.00]

Figure 1: Block model setup to incorporate cut-off grades when defining economic values.

## Using Average tab

Grades in MiningMath are controlled as a minimum and/or maximum average calculation, which means that these limits do not represent cut-off values since the algorithm can use lower values to blend higher ones. Thus, to use this approach, just set a very negative value on the grades below the cut-off so that these blocks would reduce substantially the average when processed. It can also work to constraint a contaminant maximum limit by adding a high grade on it, as it can be viewed in Figure 2Once again, the math is:

Ore_Grade1 = If [Ore_Grade] < [0.5], then [-999,999,999.00], else [Ore_Grade]

Figure 2: Block model setup to incorporate cut-off grades using average.

## Using Sum tab

Another option is by using the sum tab to control material types. Therefore, it would be required to create a field to calculate only waste blocks mass and set the constraint of the maximum limit of it in the plant as zero, as it is seen in Figure 3. It is worth mentioning that this approach could increase the complexity of the optimization due to the priority order within the algorithm.

Tonnage_Waste = If [Ore_Grade] < [0.5], then [Volume*density], else [0]

Figure 3: Block model setup to incorporate cut-off grades using sum.

## Understanding results

The mined blocks file, as seen in Figure 4, is the main output to trace the blocks from each destination, to understand the results, and to find the best way to enhance your reporting based on any detail that you wish to disclose. There are many useful tips to identify, and understand the results generated, some of them, are listed below:

• Filter results where the period mined is equal to the period processed. Check process economic values of those blocks, which were processed, identify the lower one (which means the cut-off value at the plant), and compare it with higher processing economic value of those who went to the dump.

• Calculate the average grade of any material in period mined equal to the period processed filter. Check if the blocks, which are going to dump, would have exceeded any limit in the plant, if so, even having good economic values, they would not comprise the constraints in place.

To sum up, there are a lot of validations that can be done to understand why the algorithm is taking such decisions. It is also worth mentioning that any constraint can influence the results, even geometric ones, which could change the sequence and change the destination of the block at any period.

Figure 4: Mined blocks output file.